The compound amount when an investment is compounded continuously is expressed by the formula A = Peni, where A is the compound amount, n is the number of years, and i is the interest rate per year. Find the compound amount of an investment of $2500 at an interest rate of 10% for 2 years if it is compounded continuously.
A)$3,000.00
B)$3,025.00
C)$4,023.59
D)$3,053.51

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount ($2500), $r$ is the annual interest rate (10% or 0.10), and $t$ is the time in years (2). Plugging these values into the formula gives $A = 2500e^{0.10 \times 2} = 2500e^{0.20}$. Calculating this gives $A \approx \$3,053.51$.

The Compound Amount When an Investment Is Compounded Continuously Is